Do I need other thing to do after plugged it all ?
With this battery, what is average lifespan ? to charge it again, I need to plug the Photon on micro usb port ? or how can I do ?
Last, I already use the Grove shield with the Photon, plugged like it : http://www.seeedstudio.com/depot/images/110060048%201_03.jpg
3. do you think it will work without any problem if I plug the battery shield on top of the grove shield, and the photon on top of the battery shield ?
1.) Lifespan wise, no one can be certain as it depends on the charge/discharge and usage pattern of your application
2.) You only need the battery and USB input for charging
3.) I cannot find the Grove shield that you are using. Can you paste the link so that i can see if there are issues stacking the shields?
4.) The battery you intend to use is fine
As expected but just to give you the confirmation, the mix Photon Particle / Grove Shield / Sparkfun battery shield works like a charm, just plug it and ready to play, awesome